This step is not the source of the fallacy.

This follows from the previous step, "In any group
that consists of just one person, everybody in the group has
the same age", which is statement S(1) (it's what you get by
plugging n=1 into the general statement S(n)).
Why don't you go back to the list of steps in the
proof and see if you can identify which one
is wrong, now that you know it isn't this one?
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